PolynomialRegressionTrainer

Computes coefficients for polynomial regession model.

Overview

This class is responsible for determining the coefficients of a multi-dimensional polynomial which approximates the behavior of the Quantity of Interest (QoI) in the parameter space. For this, the object needs $var element = document.getElementById("moose-equation-664621c8-4102-4095-99d4-af0fe317a684");katex.render("N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ training points in the parameters space. These training points can be characterized using their coordinates in the parameter space:

var element = document.getElementById("moose-equation-4d076de4-e3da-4aff-a27b-c2a216068f5c");katex.render("\\textbf{X} = \\begin{bmatrix} x_{1,1} & x_{1,2} & \\dots & x_{1,D} \\\\ x_{2,1} & x_{2,2} & \\dots & x_{2,D} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ x_{N,1} & x_{N,2} & \\dots & x_{N,D} \\end{bmatrix} = \\begin{bmatrix} \\textbf{x}_{1} \\\\ \\textbf{x}_{2} \\\\ \\vdots \\\\ \\textbf{x}_{N} \\end{bmatrix}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-a4263179-3d93-4279-a97e-3f1db25cb2e9");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes the dimension of the parameter space and $var element = document.getElementById("moose-equation-b6f6e3ba-f972-478e-aeda-a608e4899b70");katex.render("\\textbf{x}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a D-dimensional vector containing the coordinates in each dimension. Similarly to other Trainer classes, PolynomialRegressionTrainer accesses this matrix from a Sampler object. Of course, the trainer has to know the values of the QoI at these coordinates as well:

var element = document.getElementById("moose-equation-3ce76f33-5a30-41ab-b883-19019f2fb06b");katex.render("\\textbf{y} = \\begin{bmatrix} y_{1} \\\\ y_{2} \\\\ \\vdots\\\\ y_{N} \\end{bmatrix} .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

This data is accessed through a VectorPostprocessor. Now that all data is available, $var element = document.getElementById("moose-equation-ef7c933f-147a-48d9-8d64-dcd7d71c3cd2");katex.render("\\textbf{y}=f(\\textbf{x})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ unknown function is approximated using a polynomial expression of the following form:

(1)var element = document.getElementById("moose-equation-fa9a78ae-2058-4e45-a6e1-43bd7becabef");katex.render("\\textbf{y} \\approx \\hat{\\textbf{y}} = \\sum \\limits_{k=1}^{N_p}P(\\textbf{x}, \\textbf{i}_{k})c_k=\\textbf{P}(\\textbf{x})\\textbf{c},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-26702a0a-9e4e-445a-956a-4ddd4c3873a0");katex.render("N_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the number of polynomial terms in the approximation, $var element = document.getElementById("moose-equation-f5797d28-0d76-40a9-b041-1f634133625b");katex.render("\\textbf{c}=[c_1,...,c_{N_p}]^T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the unknown coefficients and $var element = document.getElementById("moose-equation-05df04d7-95fc-4bc3-a49c-974524b9f54c");katex.render("\\textbf{P}(\\textbf{x})=[P(\\textbf{x}, \\textbf{i}_{1}),...,P(\\textbf{x}, \\textbf{i}_{N_p})]", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The used polynomials in this case can be defined as

var element = document.getElementById("moose-equation-65c635f2-a53a-42df-952c-c380beabb0d9");katex.render("P(\\textbf{x}, \\textbf{i}) = \\textbf{x}^\\textbf{i} = \\prod \\limits_{j=1}^D x_j^{i_j},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-93966c96-e515-4594-aff2-0d648afb4a72");katex.render("x_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes the $var element = document.getElementById("moose-equation-ccce6a7f-a51f-491a-8f15-53c10ef4f8da");katex.render("j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ -th coordinate of parameter vector $var element = document.getElementById("moose-equation-a85846bf-4788-4358-bcd4-b82aab79c376");katex.render("\\textbf{x}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , while $var element = document.getElementById("moose-equation-17c09e12-8826-4373-9f81-44627275d302");katex.render("\\textbf{i}=(i_1,...,i_D)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a $var element = document.getElementById("moose-equation-4900ee41-c4fe-43e7-820e-3daf147abda2");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ -dimensional tuple containing the powers for each coordinate. This tuple is the same as described in PolynomialChaos. To determine these tuples, the trainer needs an additional input parameter, namely the maximum degree of the polynomial. This limits the number of polynomial terms in Eq. (1). If this number is fixed, the only unknown parameters are the elements of $var element = document.getElementById("moose-equation-70ce1b62-7b8b-472f-a858-c3ff8cb69c87");katex.render("\\textbf{c}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

To determine these, a regression matrix can be defined as:

var element = document.getElementById("moose-equation-08f3b2f4-5eb9-4e94-97da-4809e1e6de82");katex.render("\\textbf{R} = \\begin{bmatrix} \\textbf{P}(\\textbf{x}_1) \\\\ \\textbf{P}(\\textbf{x}_2) \\\\ \\vdots \\\\ \\textbf{P}(\\textbf{x}_{N}) \\end{bmatrix}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Ordinary Least Squares (OLS) regression

Using regression matrix $var element = document.getElementById("moose-equation-bfc31d7a-ec21-4164-928f-19ab75038e56");katex.render("\\textbf{R}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and Ordinary Least Squares (OLS) approach described on Wikipedia in detail, the unknown coefficients can be determined as follows:

var element = document.getElementById("moose-equation-a3a3cb21-4a3a-4163-9de9-7ac9e7bcd9a1");katex.render("\\textbf{c}=\\left(\\textbf{R}^T\\textbf{R}\\right)^{-1}\\textbf{R}^T\\textbf{y}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Finally, it must be mentioned that this method is only applicable if $var element = document.getElementById("moose-equation-c10871a3-ad08-40bf-8f8e-21afbdd10dfe");katex.render("N_p \\leq N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and keeping $var element = document.getElementById("moose-equation-8ca71327-177b-4fd0-ba3d-77a973faf1fb");katex.render("N_p << N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is recommended.

Ridge regression

Unfortunately, the OLS approach is known to have some issues like: - It is prone to overfit the data, - It yields inaccurate results if the input variables are correlated, - It is sensitive to outliers.

To tackle the problem, an $var element = document.getElementById("moose-equation-e457f93c-9480-4696-bc96-cc643f83caeb");katex.render("L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ regularization (or Tikhonov regularization is adopted to make sure that the coefficients of the expansion do have uncontrollably high values. This extended least squares regression is often referred to as Ridge Regression. In this scenario the coefficients can be determined by solving:

var element = document.getElementById("moose-equation-fc0314c9-11e6-46da-ab4b-7ec0061f6b4a");katex.render("\\textbf{c}=\\left(\\textbf{R}^T\\textbf{R}+\\lambda I\\right)^{-1}\\textbf{R}^T\\textbf{y},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-8e67a654-73fc-4532-90e4-fb535e100304");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a penalty parameter which penalizes coefficients with large magnitudes. As $var element = document.getElementById("moose-equation-ed99f607-2a52-4577-9e13-c36e5783a8a4");katex.render("\\lambda \\rightarrow 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , Ridge regression converges to OLS.

Example Input File Syntax

To get the necessary data, two essential blocks have to be included in the master input file. The first, the sampler defined in Samplers, creates the coordinates in matrix $var element = document.getElementById("moose-equation-0ffaa90a-ebee-4247-a81c-f7d8a85b6b14");katex.render("\\textbf{X}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , while the objects in VectorPostprocessors create, fill and store the result vector $var element = document.getElementById("moose-equation-6731b27e-4b13-4260-a484-029b43c15247");katex.render("\\textbf{y}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

[Samplers<<<{"href": "../../syntax/Samplers/index.html"}>>>]
  [sample]
    type = CartesianProduct<<<{"description": "Provides complete Cartesian product for the supplied variables.", "href": "../samplers/CartesianProductSampler.html"}>>>
    linear_space_items<<<{"description": "A list of triplets, each item should include the min, step size, and number of steps."}>>> = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors<<<{"href": "../../syntax/VectorPostprocessors/index.html"}>>>]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

Similarly to NearestPointTrainer, a GFunction vector postprocessor from SobolStatistics is used to emulate a full-order model. This simply evaluates a function at sample points.

Using this data and the maximum degree setting (max_degree in the input file), the trainer computes the model coefficients $var element = document.getElementById("moose-equation-8fefc2d6-974d-405c-90b2-1848f0d2529e");katex.render("\\textbf{c}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . To control the type of regression, the user has to set regression_type to either 'ols' or 'ridge' in the input file:

[Trainers<<<{"href": "../../syntax/Trainers/index.html"}>>>]
  [train]
    type = PolynomialRegressionTrainer<<<{"description": "Computes coefficients for polynomial regession model.", "href": "PolynomialRegressionTrainer.html"}>>>
    regression_type<<<{"description": "The type of regression to perform."}>>> = "ols"
    sampler<<<{"description": "Sampler used to create predictor and response data."}>>> = sample
    response<<<{"description": "Reporter value of response results, can be vpp with <vpp_name>/<vector_name> or sampler column with 'sampler/col_<index>'."}>>> = values/g_values
    max_degree<<<{"description": "Maximum polynomial degree to use for the regression."}>>> = 3
  []
[]

Input Parameters

max_degreeMaximum polynomial degree to use for the regression.
C++ Type:unsigned int
Controllable:No
Description:Maximum polynomial degree to use for the regression.
regression_typeThe type of regression to perform.
C++ Type:MooseEnum
Options:ols, ridge
Controllable:No
Description:The type of regression to perform.
responseReporter value of response results, can be vpp with / or sampler column with 'sampler/col_'.
C++ Type:ReporterName
Controllable:No
Description:Reporter value of response results, can be vpp with / or sampler column with 'sampler/col_'.
samplerSampler used to create predictor and response data.
C++ Type:SamplerName
Controllable:No
Description:Sampler used to create predictor and response data.

Required Parameters

converged_reporterReporter value used to determine if a sample's multiapp solve converged.
C++ Type:ReporterName
Controllable:No
Description:Reporter value used to determine if a sample's multiapp solve converged.
cv_n_trials1Number of repeated trials of cross-validation to perform.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Number of repeated trials of cross-validation to perform.
cv_seed4294967295Seed used to initialize random number generator for data splitting during cross validation.
Default:4294967295
C++ Type:unsigned int
Controllable:No
Description:Seed used to initialize random number generator for data splitting during cross validation.
cv_splits10Number of splits (k) to use in k-fold cross-validation.
Default:10
C++ Type:unsigned int
Controllable:No
Description:Number of splits (k) to use in k-fold cross-validation.
cv_surrogateName of Surrogate object used for model cross-validation.
C++ Type:UserObjectName
Controllable:No
Description:Name of Surrogate object used for model cross-validation.
cv_typenoneCross-validation method to use for dataset. Options are 'none' or 'k_fold'.
Default:none
C++ Type:MooseEnum
Options:none, k_fold
Controllable:No
Description:Cross-validation method to use for dataset. Options are 'none' or 'k_fold'.
filenameThe name of the file which will be associated with the saved/loaded data.
C++ Type:FileName
Controllable:No
Description:The name of the file which will be associated with the saved/loaded data.
penalty0Penalty for Ridge regularization.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Penalty for Ridge regularization.
predictor_colsSampler columns used as the independent random variables, If 'predictors' and 'predictor_cols' are both empty, all sampler columns are used.
C++ Type:std::vector<unsigned int>
Controllable:No
Description:Sampler columns used as the independent random variables, If 'predictors' and 'predictor_cols' are both empty, all sampler columns are used.
predictorsReporter values used as the independent random variables, If 'predictors' and 'predictor_cols' are both empty, all sampler columns are used.
C++ Type:std::vector<ReporterName>
Controllable:No
Description:Reporter values used as the independent random variables, If 'predictors' and 'predictor_cols' are both empty, all sampler columns are used.
response_typerealResponse data type.
Default:real
C++ Type:MooseEnum
Options:real, vector_real
Controllable:No
Description:Response data type.
skip_unconverged_samplesFalseTrue to skip samples where the multiapp did not converge, 'stochastic_reporter' is required to do this.
Default:False
C++ Type:bool
Controllable:No
Description:True to skip samples where the multiapp did not converge, 'stochastic_reporter' is required to do this.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_train.i)
(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/errors/error.i)
(modules/stochastic_tools/examples/surrogates/cross_validation/all_trainers_uniform_cv.i)
(modules/stochastic_tools/test/tests/auxkernels/surrogate_scalar_aux/surrogate_scalar_aux.i)
(modules/stochastic_tools/examples/workshop/step06.i)
(modules/stochastic_tools/test/tests/userobjects/inverse_mapping/create_mapping_main.i)
(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train_and_evaluate.i)
(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train.i)
(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/poly_reg_vec.i)
(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_trainer.i)
(modules/stochastic_tools/test/tests/auxkernels/surrogate_aux/surrogate.i)
(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_train.i)
(modules/stochastic_tools/test/tests/surrogates/cross_validation/train_and_cv.i)
(modules/stochastic_tools/test/tests/surrogates/cross_validation/poly_reg_vec.i)

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'train'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'train'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'train'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/normal_train.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [q_dist]
    type = Normal
    mean = 10000
    standard_deviation = 500
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
  [Tinf_dist]
    type = Normal
    mean = 300
    standard_deviation = 10
  []
[]

[Samplers]
  [pc_sampler]
    type = Quadrature
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [pr_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 6560
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [pc_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pc_sampler
  []
  [pr_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pr_sampler
  []
[]

[Controls]
  [pc_cmdline]
    type = MultiAppSamplerControl
    multi_app = pc_sub
    sampler = pc_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = pr_sub
    sampler = pr_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [pc_data]
    type = SamplerReporterTransfer
    from_multi_app = pc_sub
    sampler = pc_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
  [pr_data]
    type = SamplerReporterTransfer
    from_multi_app = pr_sub
    sampler = pr_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
[]

[Trainers]
  [pc_max]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    sampler = pc_sampler
    response = results/pc_data:max:value
  []
  [pr_max]
    type = PolynomialRegressionTrainer
    execute_on = timestep_end
    regression_type = "ols"
    max_degree = 4
    sampler = pr_sampler
    response = results/pr_data:max:value
    []
[]

[Outputs]
  [pc_out]
    type = SurrogateTrainerOutput
    trainers = 'pc_max'
    execute_on = FINAL
  []
  [pr_out]
    type = SurrogateTrainerOutput
    trainers = 'pr_max'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/errors/error.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10'
  []
  [sample_wrong]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample_wrong
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

(modules/stochastic_tools/examples/surrogates/cross_validation/all_trainers_uniform_cv.i)

[StochasticTools]
[]

[GlobalParams]
  sampler = cv_sampler
  response = results/response_data:max:value
  cv_type = "k_fold"
  cv_splits = 5
  cv_n_trials = 100
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [L_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.05
  []
  [Tinf_dist]
    type = Uniform
    lower_bound = 290
    upper_bound = 310
  []
[]

[Samplers]
  [cv_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 1000
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [cv_sub]
    type = SamplerFullSolveMultiApp
    input_files = all_sub.i
    mode = batch-reset
  []
[]

[Controls]
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = cv_sub
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [response_data]
    type = SamplerReporterTransfer
    from_multi_app = cv_sub
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [cv_scores]
    type = CrossValidationScores
    models = 'pr_surr pc_surr np_surr gp_surr ann_surr'
    execute_on = FINAL
  []
[]

[Trainers]
  [pr_max]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    max_degree = 3
    cv_surrogate = "pr_surr"
    execute_on = timestep_end
  []
  [pc_max]
    type = PolynomialChaosTrainer
    order = 3
    distributions = "k_dist q_dist L_dist Tinf_dist"
    cv_surrogate = "pc_surr"
    execute_on = timestep_end
  []
  [np_max]
    type = NearestPointTrainer
    cv_surrogate = "np_surr"
    execute_on = timestep_end
  []
  [gp_max]
    type = GaussianProcessTrainer
    covariance_function = 'rbf'
    standardize_params = 'true'
    standardize_data = 'true'
    cv_surrogate = "gp_surr"
    execute_on = timestep_end
  []
  [ann_max]
    type = LibtorchANNTrainer
    num_epochs = 100
    num_batches = 5
    num_neurons_per_layer = '64'
    learning_rate = 1e-2
    rel_loss_tol = 1e-4
    filename = mynet.pt
    read_from_file = false
    print_epoch_loss = 0
    activation_function = 'relu'
    cv_surrogate = "ann_surr"
    standardize_input = false
    standardize_output = false
  []
[]

[Covariance]
  [rbf]
    type = SquaredExponentialCovariance
    noise_variance = 3.79e-6
    signal_variance = 1 #Use a signal variance of 1 in the kernel
    length_factor = '5.34471 1.41191 5.90721 2.83723' #Select a length factor for each parameter
  []
[]

[Surrogates]
  [pr_surr]
    type = PolynomialRegressionSurrogate
    trainer = pr_max
  []
  [pc_surr]
    type = PolynomialChaos
    trainer = pc_max
  []
  [np_surr]
    type = NearestPointSurrogate
    trainer = np_max
  []
  [gp_surr]
    type = GaussianProcessSurrogate
    trainer = gp_max
  []
  [ann_surr]
    type = LibtorchANNSurrogate
    trainer = ann_max
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/auxkernels/surrogate_scalar_aux/surrogate_scalar_aux.i)

[StochasticTools]
[]

[VectorPostprocessors]
  [reader]
    type = CSVReader
    csv_file = data.csv
  []
[]

[Samplers]
  [sample]
    type = CSVSampler
    samples_file = data.csv
    column_indices = '0 1'
    execute_on = INITIAL
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = ols
    sampler = sample
    response = reader/c
    max_degree = 2
    execute_on = INITIAL
  []
[]

[Surrogates]
  [surrogate]
    type = PolynomialRegressionSurrogate
    trainer = train
  []
[]

[AuxVariables]
  [v]
    family = SCALAR
  []

  [T]
    family = SCALAR
    initial_condition = 325
  []
[]

[AuxScalarKernels]
  [scalar_eval]
    type = SurrogateModelScalarAux
    variable = v
    model = 'surrogate'
    parameters = 'T 5'
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [Tpp]
    type = ScalarVariable
    variable = T
    execute_on = INITIAL
  []
[]

[Outputs]
  csv = true
[]

(modules/stochastic_tools/examples/workshop/step06.i)

[StochasticTools]
[]

[Samplers]
  [csv]
    type = CSVSampler
    samples_file = 'step02_out_sampling_matrix_0001.csv'
    column_names = 'D q T_0 q_0 results:T_avg:value results:q_left:value'
  []
  [resample]
    type = Cartesian1D
    linear_space_items = '0.5 0.1 21
                          50 5 21
                          200 10 21
                          -100 2 26'
    nominal_values = '1 100 300 -100'
  []
[]

[Reporters]
  [sampling_matrix]
    type = StochasticMatrix
    sampler = csv
    sampler_column_names = 'D q T_0 q_0 T_avg q_left'
    outputs = none
  []
  [pr_T_avg_cv]
    type = CrossValidationScores
    models = pr_T_avg
  []
  [evaluate]
    type = EvaluateSurrogate
    model = pr_T_avg
    sampler = resample
    parallel_type = ROOT
  []
[]

[Trainers]
  [poly_reg_T_avg]
    type = PolynomialRegressionTrainer
    sampler = csv
    predictor_cols = '0 1 2 3'
    response = sampling_matrix/T_avg
    max_degree = 3
    regression_type = OLS

    cv_type = K_FOLD
    cv_surrogate = pr_T_avg
  []
[]

[Surrogates]
  [pr_T_avg]
    type = PolynomialRegressionSurrogate
    trainer = poly_reg_T_avg
  []
[]

[Outputs]
  json = true
[]

(modules/stochastic_tools/test/tests/userobjects/inverse_mapping/create_mapping_main.i)

[StochasticTools]
[]

[Distributions]
  [S_dist]
    type = Uniform
    lower_bound = 0
    upper_bound = 10
  []
  [D_dist]
    type = Uniform
    lower_bound = 0
    upper_bound = 10
  []
[]

[Samplers]
  [sample]
    type = MonteCarlo
    num_rows = 8
    distributions = 'S_dist D_dist'
    execute_on = PRE_MULTIAPP_SETUP
    min_procs_per_row = 2
  []
[]

[MultiApps]
  [worker]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = sample
    mode = batch-reset
    min_procs_per_app = 2
  []
[]

[Trainers]
  [polyreg_v]
    type = PolynomialRegressionTrainer
    sampler = sample
    regression_type = ols
    max_degree = 1
    response = reduced_solutions/v_pod_mapping
    response_type = vector_real
    execute_on = FINAL
  []
  [polyreg_v_aux]
    type = PolynomialRegressionTrainer
    sampler = sample
    regression_type = ols
    max_degree = 1
    response = reduced_solutions/v_aux_pod_mapping
    response_type = vector_real
    execute_on = FINAL
  []
[]

[VariableMappings]
  [pod_mapping]
    type = PODMapping
    solution_storage = parallel_storage
    variables = "v v_aux"
    num_modes_to_compute = '8 8'
    extra_slepc_options = "-svd_monitor_all"
  []
[]

[Transfers]
  [param_transfer]
    type = SamplerParameterTransfer
    to_multi_app = worker
    sampler = sample
    parameters = 'Kernels/source_v/value BCs/right_v/value'
  []
  [solution_transfer]
    type = SerializedSolutionTransfer
    parallel_storage = parallel_storage
    from_multi_app = worker
    sampler = sample
    solution_container = solution_storage
    variables = 'v'
    serialize_on_root = false
  []
  [solution_transfer_aux]
    type = SerializedSolutionTransfer
    parallel_storage = parallel_storage
    from_multi_app = worker
    sampler = sample
    solution_container = solution_storage_aux
    variables = 'v_aux'
    serialize_on_root = false
  []
[]

[Controls]
  [cmd_line]
    type = MultiAppSamplerControl
    multi_app = worker
    sampler = sample
    param_names = 'S D'
  []
[]

[Reporters]
  [parallel_storage]
    type = ParallelSolutionStorage
    variables = 'v v_aux'
    outputs = none
  []
  [reduced_solutions]
    type = MappingReporter
    sampler = sample
    parallel_storage = parallel_storage
    mapping = pod_mapping
    variables = "v v_aux"
    execute_on = timestep_end # To make sure the trainer sees the results on FINAL
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
  [mapping]
    type = MappingOutput
    mappings = pod_mapping
    execute_on = FINAL
  []
  [rom]
    type = SurrogateTrainerOutput
    trainers = 'polyreg_v polyreg_v_aux'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train_and_evaluate.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10'
  []
  [test]
    type = CartesianProduct
    linear_space_items = '0.25 0.5 20'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Reporters]
  [results]
    type = EvaluateSurrogate
    model = surrogate
    sampler = test
    execute_on = final
    parallel_type = ROOT
  []
[]

[Surrogates]
  [surrogate]
    type = PolynomialRegressionSurrogate
    trainer = train
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

[Outputs]
  csv = true
  execute_on = FINAL
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/train.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 1 10
                          0 1 10
                          0 1 10'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0 0 0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'train'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/polynomial_regression/poly_reg_vec.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist L_dist'
    execute_on = PRE_MULTIAPP_SETUP
    min_procs_per_row = 2
  []
[]

[GlobalParams]
  sampler = sample
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub_vector.i
    mode = batch-reset
    execute_on = initial
    min_procs_per_app = 2
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    param_names = 'Materials/conductivity/prop_values L'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    stochastic_reporter = results
    from_reporter = 'T_vec/T T_vec/x'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [eval]
    type = EvaluateSurrogate
    model = pr_surrogate
    response_type = vector_real
    parallel_type = ROOT
    execute_on = timestep_end
  []
[]

[Trainers]
  [pr]
    type = PolynomialRegressionTrainer
    regression_type = ols
    max_degree = 2
    response = results/data:T_vec:T
    response_type = vector_real
    execute_on = initial
  []
[]

[Surrogates]
  [pr_surrogate]
    type = PolynomialRegressionSurrogate
    trainer = pr
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = timestep_end
  []
[]

(modules/stochastic_tools/examples/surrogates/combined/trans_diff_2d/trans_diff_trainer.i)

[StochasticTools]
[]

[Distributions]
  [C_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.02
  []
  [f_dist]
    type = Uniform
    lower_bound = 15
    upper_bound = 25
  []
  [init_dist]
    type = Uniform
    lower_bound = 270
    upper_bound = 330
  []
[]

[Samplers]
  [sample]
    type = Quadrature
    order = 5
    distributions = 'C_dist f_dist init_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [runner]
    type = SamplerFullSolveMultiApp
    input_files = 'trans_diff_sub.i'
    sampler = sample
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = runner
    sampler = sample
    param_names = 'Materials/diff_coeff/constant_expressions Functions/src_func/vals Variables/T/initial_condition'
  []
[]

[Transfers]
  [results]
    type = SamplerReporterTransfer
    from_multi_app = runner
    sampler = sample
    stochastic_reporter = trainer_results
    from_reporter = 'time_max/value time_min/value'
  []
[]

[Reporters]
  [trainer_results]
    type = StochasticReporter
  []
[]

[Trainers]
  [pc_max]
    type = PolynomialChaosTrainer
    execute_on = final
    order = 5
    distributions = 'C_dist f_dist init_dist'
    sampler = sample
    response = trainer_results/results:time_max:value
  []
  [pc_min]
    type = PolynomialChaosTrainer
    execute_on = final
    order = 5
    distributions = 'C_dist f_dist init_dist'
    sampler = sample
    response = trainer_results/results:time_min:value
  []
  [np_max]
    type = NearestPointTrainer
    execute_on = final
    sampler = sample
    response = trainer_results/results:time_max:value
  []
  [np_min]
    type = NearestPointTrainer
    execute_on = final
    sampler = sample
    response = trainer_results/results:time_min:value
  []
  [pr_max]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    execute_on = final
    max_degree = 4
    sampler = sample
    response = trainer_results/results:time_max:value
  []
  [pr_min]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    execute_on = final
    max_degree = 4
    sampler = sample
    response = trainer_results/results:time_min:value
  []
[]

[Outputs]
  [out]
    type = SurrogateTrainerOutput
    trainers = 'pc_max pc_min np_max np_min pr_max pr_min'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/auxkernels/surrogate_aux/surrogate.i)

[StochasticTools]
[]

[Distributions]
  [uniform]
    type = Uniform
    lower_bound = 0
    upper_bound = 1
  []
[]

[Samplers]
  [mc]
    type = MonteCarlo
    distributions = 'uniform uniform uniform uniform'
    num_rows = 50
  []
[]

[GlobalParams]
  sampler = mc
[]

[MultiApps]
  [model]
    type = SamplerFullSolveMultiApp
    input_files = model.i
    mode = batch-restore
    no_restore = true
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = model
    parameters ='Postprocessors/x1/value Postprocessors/x2/value Postprocessors/x3/value Postprocessors/x4/value'
  []
  [data]
    type = SamplerReporterTransfer
    from_multi_app = model
    stochastic_reporter = storage
    from_reporter = 'val/value'
  []
[]

[Reporters]
  [storage]
    type = StochasticReporter
  []
[]

[Trainers]
  [poly_regression]
    type = PolynomialRegressionTrainer
    regression_type = ols
    max_degree = 2
    response = storage/data:val:value
  []
[]

[Outputs]
  [trainer]
    type = SurrogateTrainerOutput
    trainers = poly_regression
  []
[]

(modules/stochastic_tools/examples/surrogates/polynomial_regression/uniform_train.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Uniform
    lower_bound = 1
    upper_bound = 10
  []
  [q_dist]
    type = Uniform
    lower_bound = 9000
    upper_bound = 11000
  []
  [L_dist]
    type = Uniform
    lower_bound = 0.01
    upper_bound = 0.05
  []
  [Tinf_dist]
    type = Uniform
    lower_bound = 290
    upper_bound = 310
  []
[]

[Samplers]
  [pc_sampler]
    type = Quadrature
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
  [pr_sampler]
    type = LatinHypercube
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    num_rows = 6560
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[MultiApps]
  [pc_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pc_sampler
  []
  [pr_sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = pr_sampler
  []
[]

[Controls]
  [pc_cmdline]
    type = MultiAppSamplerControl
    multi_app = pc_sub
    sampler = pc_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
  [pr_cmdline]
    type = MultiAppSamplerControl
    multi_app = pr_sub
    sampler = pr_sampler
    param_names = 'Materials/conductivity/prop_values Kernels/source/value Mesh/xmax BCs/right/value'
  []
[]

[Transfers]
  [pc_data]
    type = SamplerReporterTransfer
    from_multi_app = pc_sub
    sampler = pc_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
  [pr_data]
    type = SamplerReporterTransfer
    from_multi_app = pr_sub
    sampler = pr_sampler
    stochastic_reporter = results
    from_reporter = 'max/value'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
  []
[]

[Trainers]
  [pc_max]
    type = PolynomialChaosTrainer
    execute_on = timestep_end
    order = 8
    distributions = 'k_dist q_dist L_dist Tinf_dist'
    sampler = pc_sampler
    response = results/pc_data:max:value
  []
  [pr_max]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    execute_on = timestep_end
    max_degree = 4
    sampler = pr_sampler
    response = results/pr_data:max:value
  []
[]

[Outputs]
  [pc_out]
    type = SurrogateTrainerOutput
    trainers = 'pc_max'
    execute_on = FINAL
  []
  [pr_out]
    type = SurrogateTrainerOutput
    trainers = 'pr_max'
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/cross_validation/train_and_cv.i)

[StochasticTools]
[]

[Samplers]
  [sample]
    type = CartesianProduct
    linear_space_items = '0 0.1515151515 100'
  []
[]

[VectorPostprocessors]
  [values]
    type = GFunction
    sampler = sample
    q_vector = '0'
    execute_on = INITIAL
    outputs = none
  []
[]

[Surrogates]
  [surrogate]
    type = PolynomialRegressionSurrogate
    trainer = train
  []
[]

[Trainers]
  [train]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = values/g_values
    max_degree = 3
    cv_type = "k_fold"
    cv_splits = 2
    cv_n_trials = 3
  []
[]

[Reporters]
  [cv_scores]
    type = CrossValidationScores
    models = 'surrogate'
    execute_on = FINAL
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
[]

(modules/stochastic_tools/test/tests/surrogates/cross_validation/poly_reg_vec.i)

[StochasticTools]
[]

[Distributions]
  [k_dist]
    type = Normal
    mean = 5
    standard_deviation = 2
  []
  [L_dist]
    type = Normal
    mean = 0.03
    standard_deviation = 0.01
  []
[]

[Samplers]
  [sample]
    type = LatinHypercube
    num_rows = 10
    distributions = 'k_dist L_dist'
    execute_on = PRE_MULTIAPP_SETUP
  []
[]

[GlobalParams]
  sampler = sample
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub_vector.i
    mode = batch-reset
    execute_on = initial
  []
[]

[Controls]
  [cmdline]
    type = MultiAppSamplerControl
    multi_app = sub
    param_names = 'Materials/conductivity/prop_values L'
  []
[]

[Transfers]
  [data]
    type = SamplerReporterTransfer
    from_multi_app = sub
    stochastic_reporter = results
    from_reporter = 'T_vec/T T_vec/x'
  []
[]

[Reporters]
  [results]
    type = StochasticReporter
    outputs = none
  []
  [cv_scores]
    type = CrossValidationScores
    models = pr_surrogate
    execute_on = FINAL
  []
[]

[Trainers]
  [pr_trainer]
    type = PolynomialRegressionTrainer
    regression_type = "ols"
    sampler = sample
    response = results/data:T_vec:T
    response_type = vector_real
    execute_on = timestep_end
    max_degree = 1
    cv_type = "k_fold"
    cv_splits = 2
    cv_n_trials = 3
    cv_surrogate = pr_surrogate
    cv_seed = 1
  []
[]

[Surrogates]
  [pr_surrogate]
    type = PolynomialRegressionSurrogate
    trainer = pr_trainer
  []
[]

[Outputs]
  [out]
    type = JSON
    execute_on = FINAL
  []
[]

Overview
Ordinary Least Squares ( OLS ) regression
Ridge regression
Example Input File Syntax
Input Parameters
Input Files